Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Writing Equations of a Line

2.
Various Forms of an Equation of a
Line.
Slope-Intercept Form
Standard Form
Point-Slope Form
slope of the line
intercept
y mx b
m
b y
= +
=
= −
, , and are integers
0, must be postive
Ax By C
A B C
A A
+ =
>
( )
( )
1 1
1 1
slope of the line
, is any point
y y m x x
m
x y
− = +
=
-
-

3.
KEY CONCEPT
Writing an Equation of a Line
– Given slope m and y-intercept b
• Use slope-intercept form y=mx+b
– Given slope m and a point (x1,y1)
• Use point-slope form
– y - y1 = m ( x – x1)
• Given points (x1,y1) and (x2,y2)
– Find your slope then use point-slope form with either point.

4.
Write an equation given the slope and y-interceptEXAMPLE 1
Write an equation of the line shown.

5.
SOLUTION
Write an equation given the slope and y-interceptEXAMPLE 1
From the graph, you can see that the slope is m =
and the y-intercept is b = –2. Use slope-intercept form
to write an equation of the line.
3
4
y = mx + b Use slope-intercept form.
y = x + (–2)
3
4
Substitute for m and –2 for b.
3
4
y = x –2
3
4
Simplify.

7.
Write an equation given the slope and a pointEXAMPLE 2
Write an equation of the line that passes
through (5, 4) and has a slope of –3.
Because you know the slope and a point on the
line, use point-slope form to write an equation of
the line. Let (x1, y1) = (5, 4) and m = –3.
y – y1 = m(x – x1) Use point-slope form.
y – 4 = –3(x – 5) Substitute for m, x1, and y1.
y – 4 = –3x + 15 Distributive property
SOLUTION
y = –3x + 19 Write in slope-intercept form.

8.
EXAMPLE 3
Write an equation of the line that passes through (–2,3)
and is (a) parallel to, and (b) perpendicular to, the line
y = –4x + 1.
SOLUTION
a. The given line has a slope of m1 = –4. So, a line
parallel to it has a slope of m2 = m1 = –4. You know
the slope and a point on the line, so use the point-
slope form with (x1, y1) = (–2, 3) to write an equation
of the line.
Write equations of parallel or perpendicular lines

11.
GUIDED PRACTICE for Examples 2 and 3GUIDED PRACTICE
4. Write an equation of the line that passes through
(–1, 6) and has a slope of 4.
y = 4x + 10
5. Write an equation of the line that passes through
(4, –2) and is (a) parallel to, and (b) perpendicular
to, the line y = 3x – 1.
y = 3x – 14ANSWER
ANSWER